Drilling assembly deflection apparatus

ABSTRACT

An apparatus for deflecting the axis of a drill assembly has a housing and a central shaft inside said housing where the shaft has spaced surfaces contoured into the outer surface of the shaft. Means are included for yieldably attaching one end of the shaft to the outer housing. Engaging means are mounted rigidly to the interior of the outer housing and in slidable contact with the contoured spaced surfaces. Means are also provided for moving the shaft along the length of its axis so that the contoured variations will cause a change in the alignment of the outer housing with respect to the axis of the shaft.

United States Patent I [191 Dahl -et al.

[ Dec. 10, 1974 DRILLING ASSEMBLY DEFLECTION APPARATUS [75] Inventors: Hilbert D. Dahl, Ponca City, Okla;

Gordon R. Haworth, Glencoe, 11].; Tibor O. Edmond, Ponca City, Okla.

[73] Assignee: Continental Oil Company, Ponca City, Okla.

[22] Filed: Mar. 12, 1973 [21] Appl. N0.: 340,639

[52] US. Cl 175/73, 175/24, 175/61 [51] Int. Cl E21b 7/04 [58] Field of Search 175/24, 26, 41, 61, 62,

[56] References Cited UNITED STATES PATENTS 3,043,381 7/1962 McNeely 175/73 3,141,512 7/1964 Gaskell et al.... 175/61 X 3,326,008 6/1967 Baran et a]. 175/61 X 3,526,285 9/1970 Adkins et al 175/73 3,554,301 l/l97l Adkins et al 175/24 3,587,756 6/1971 Adkins et a1 175/61 3,593,810 7/1971 Fields 175/61 3,630,295 12/1971 Coyne et al 175/73 7/1972 Kostylev et a]. l75/6l X Primary ExaminerDavid H. Brown Attorney, Agent, or FirmWilliam J. Miller 571 ABSTRACT An apparatus for deflecting the axis of a drill assembly has a housing and a central shaft inside said housing where the shaft has spaced surfaces contoured into the outer surface of the shaft. Means are included for yieldably attaching one end of the shaft to the outer housing. Engaging means are mounted rigidly to the interior of the outer housing and in slidable contact with the contoured spaced surfaces. Means are also provided for moving the shaft along the length of its axis so that the contoured variations will cause a change in the alignment of the outer housing with respect to the axis of the shaft.

19 Claims, 9 Drawing Figures PATENTE LZE 1 01974 SHEET 2 BF 3 KOPOE oEhowJm v his 158 i v 6528 1 DRILLING ASSEMBLY DEFLECTION APPARATUS BACKGROUND OF THE INVENTION In drilling either a vertical or horizontal bore hole, it may become necessary to divert the direction of the drill. In the case of a vertical bore hole, the diversion is generally accomplished by mechanical means, such as a whipstock. Such devices are acceptable when only a few diversions are required to drill the hole; however, when the drill must be continuously guided, the use of a mechanical diverter, such as a whipstock, becomes uneconomical, since the drill and its associated equipment must be removed from the bore hole each time the whipstock is inserted.

This invention relates to a method for drilling a horizontal'bore hole wherein the drill axis may be altered many times before the bore hole is completed. In patent application Ser. No. 246,297, filed Apr. 21, 1972, for Drill Hole Guidance System by Haworth- Edmond-Poundstone. A system is described for determining the locaton of a drilling assembly in relationship to the top and the bottom of a seam of coal. Means are provided to guide the drill by deflecting the axis of the drill so that the assembly will always maintain a predetermined distance from the top or the bottom of the seam. This invention relates to an improved method for deflecting the axis of a drilling assembly through 360, that is, the assembly cannot only be deflected up or down but in any other direction as well.

BRIEF DESCRIPTION OF THE PRIOR ART The patents relating to the above system generally fall into two categories. The first category is those patents which permit deflection through a single-plane and accomplish the deflection by some mechanical piston, arm, or the like. An example of this type patent is U.S. Pat. No. 3,326,008 to Baran et al. The second category of patents relates to devices for changing the direction of the drill through 360. These inventions generally accomplish the change by the movement of pistons and the like which contact the bore hole wall. The amount of extension of each of the pistons will determine the direction the drill will take. Patents illustrative of the above are issued to Gaskell et al., US. Pat. No. 3,141,512; Kostylev et al., US. Pat. No. 3,677,354; and Fields, US Pat. No. 3,593,810. In the second category also falls most large tunneling machines which have adjustable supports for orienting the axis of the drilling head of the machines with respect to the axis of the previous tunnel drilled. This disclosure illustrates a method for providing a 360 control over the drilling axis with a minimum control system which greatly simplifies the apparatus over that disclosed in any of the prior art patents.

BRIEF DESCRIPTION OF THE FIGURES apparatus;

FIG. 5 is a perspective view of the preferred embodiment of the control surface;

FIG. 6 is a cross-sectional view taken through lines 6-6 of FIG. 4;

FIG. 7 is a perspective view of a second embodiment of the control surface illustrated in FIG. 5;

FIG. 8 is a two-dimensioned control surface embodiment; and

FIG. 9 is a cross-sectional portion of FIG. 4 illustrat ing a modified placement of the contoured surfaces.

The same numbers will be used for identical parts throughout all of the drawings. I

Referring to all of the drawings but in particular to FIGS. 1 through 3, a horizontal thrust unit having a first portion 10 and a second portion 11 is interconnected by means of hydraulic piston shafts 12 and 13. Interconnecting hollow shaft 13 is connected axially and rigidly to directional control apparatus 14. Drilling apparatus 15 is rigidly coupled to position sensing appratus 17 and contains a drill 16 at its terminus.

The thrust unit comprising first portion 10 and second portion 11 provides a means for applying pressure to drill 16. Thrust unit 10 comprises a plurality of pressure pads-20 on first portion 10 and 21 on second portion 11. Unit 11 contains internally, a hydraulic piston (not shown) which is coupled to shaft 13. A plurality of similar hydraulic pistons is also coupled to each of the pads 20 and 21. Drilling assembly 15 comprises an electric motor 22 and an output shaft 23 which is coupled to the drill shank 24. A mud source 25 is connected through a pipe 26 through an opening 27 in the thrust units 10 and 1 1, through an opening 28 in deflection unit 14 and through opening 29 to outlet holes 30. Flowing out of outlet holes 30, the mud passes between the motor 22 and the housing 31 to the opening 32 in the drill shaft. The mud is expelled in openings at the terminus of the drill (not shown).

THRUST UNIT The thrust apparatus which comprises units 10 and 11, pads 20 and 21, and piston shaft 13 has thrust control inlet pipes 35 and thrust control outlet pipes 36. Said pipes are connected to thrust control system 37. The unit operates as follows:

Hydraulic pressure is applied to inlet pipes 35, applying hydraulic pressure to the piston contained in unit 11, said piston being attached to shaft 13. Simultaneously, the pads 21 are forced outwardly against the side of the bore hole. Hydraulic fluid will then increase the pressure against the piston inside unit 11, moving shaft 13 through the unit in a direction to apply power to drill bit 16. When shaft 13 has moved its maximum distance, pressure is removed from the'inlet pipes 35 and applied to the second of the inlet pipes 35. Pressure in the second pipes 35 will cause pads 20 to move outwardly and engage the wall, rigidly securing unit 10. Pressure will then be simultaneously applied to the other side of the piston inside unit 11. Pads 21 will be in the retracted state, causing unit 11 to move back into the original position so that it can reapply pressure to hollow shaft 13.

POSITION SENSING APPARATUS Position sensing apparatus 17 is illustrated as being attached to the housing oldirectional control apparatus 14. No particular location is absolutely necessary for the placement of the position sensing apparatus,

however; and it may be placed before or after the direc tional control apparatus. Position sensing apparatus 17 contains a horizontal sensor 40, a vertical sensor 41, and a roll sensor 42 along with the necessary control modules 43 and 44. The equipment used in the position sensing apparatus is well known and will not be further described. I

The vertical sensor, however, may be a radioactive source capable of detecting the position of the drilling assembly in the coal seam. The preferred embodiment utilizes a vertical sensor which detects secondary radiation caused by radioactive shale above and below the coal seam. Suitable electrical cables 45 connect the position sensing apparatus to an instrumentation readout panel 46.

DRILLING APPARATUS The drilling apparatus comprises, in the embodiment shown, an electric motor 22 which is connected through a shaft 23 to the shank 24 of a drill bit 16. The electric motor is powered by suitable electric cables 47 to a motor power source 48.

. DIRECTIONAL CONTROL APPARATUS The directional control apparatus is illustrated in detail in FIG. 4 and essentially comprises an inner hollow mandrel 50 attached to a tapered mandrel 51 which in turn is used to mount the directional control apparatus to the preceding unit which, in the above-disclosed embodiment, is the thrust unit. An outer tubular piston cylinder 52 is attached to tapered mandrel 51 by any suitable means such as threads or pins, for example.

Mounted between tubular piston cylinder 52 and hollow mandrel 50 is a tubular piston 53 having a plurality of contoured surfaces 54 formed in its outer periphery. Enclosing the directional control apparatus is an outer casing or housing 55 which is yieldably attached to tubular piston cylinder 52 at one end by means of screws 56 which pass through enlarged openings 57 and are TABLE 1 Surface A" Surface 8'' Surface C" X Y X Y X Y TABLE 2 Surface A Surface B Surface C" X Y X Y X Y secured by means of flexible-type washers 58. Between housing 55 and tubular piston 53 is mounted an engaging means 60. Engaging means 60 essentially comprises a ring 61 which is attached to housing 55 by means of a screw 62. A plurality of rollers 63 (one for each contoured surface 54) is journaled in ring 61 by a shaft 64. A biasing spring is mounted between an end flange 71 which is attached to mandrel 50 at its terminus and a secondary flange 72 which engages the end of tubular piston 53 and is freeto slide over the outer surface of mandrel 50. The end of tubular housing 55 is sealed by an end plate 75. A tubular portion 76 is axially attached to end plate and has an extension 77. Flange 71 likewise has an extension 78. A flexible rubber pipe 79 seals extension 78 to extension 77 and is retained by bands 80 and 81, respectively. Tubular piston 53 has a plurality of outerseals 82 and inner seals 83. A hydraulic inlet pipe is connected by means of a V groove 91 in tubular piston cylinder 52 to a conduit 92 to the end of tubular piston 53.

It should be noted that the outer diameter of tubular piston cylinder 52 is tapered from its mounting to its terminus 93 to provide for freedom of movement of the housing 55 through 360 without striking the outer diameter of tubular piston cylinder 52, and providing an axial movement of approximately 0.8 of a degree.

Contoured surfaces 54 in the preferred embodiment are formed in three places around the circumference of piston 53. The surfaces are designed so that axial movement along the mandrel 50 will cause deflection of the outer housing continuously from an axially aligned position to a 360 rotation. The preferred embodiment accomplishes the above by generating flat surfaces which are the mathematical equivalent of a helix. Tables 1 through 6 provide the mathematical development of each of the surfaces as measured along the length of the mandrel from point 95 to point 96.

TABLE 3 TABLE 5 Surface A" urfgcc 13" SurfmC Surface "A" Surface B Surface C" X Y X Y X Y X Y X Y X Y TABLE 4 TABLE 6 5.21m may? "B" 5.11m C" Surface A Surface 8" Surface C X .Y X Y X Y X Y X Y Y The above tables are computed on the basis of roller 63 being 0.25 inch in diameter and the surfaces being formed by a milling cutter having the same diameter as the rollers. If different diameter rollers are utilized or a different diameter millingcutter used .to form the surfaces, then the tables must be modified to accommodate the above set out variations.

OPERATION The directional controlapparatus illustrated in FIGS.

1 and 4 through 6 operates as follows:

Hydraulic pressure applied thorugh pipe 90 is applied to V-shaped groove 91, conduit 92 and into the chamber formed by tubular piston 52 and hollow mandrel 50. Hydraulic pressure, when applied to the face of piston 53, will cause the piston to move in the direction of the spring. The distance it will move will be determined by the frictional lossesin the system and by the spring bias supplied by spring 70. In the unpressured state, rollers 63 will be all equal distance from the axis 98, thereby causing the axis of housing 55 to coincide with axis98, resulting in the electric drill and bit 14 drilling a straight hole. If it is desired to deflect the direction of the drill, hydraulic fluid filling tube 90 will be pressured, forcing piston 53 to move by an amount necessary to balance the bias on spring 70. Rollers 63 following contoured surfaces 54 will be moved in accordance with these contoured surfaces. As they are moved, this movement is communicated to ring 61 which, as previously mentioned, is rigidly secured to housing 55. Thus the axis of housing 55 will be deflected in a direction corresponding to the contoured surfaces. The amount of the deflection is fixed by the particular magnitude of the contoured surface deviations. Since the contoured surfaces are mathematically equivalent to a helix, the angular deflection will move through 360. The actual direction the drill is-taking will be indicated by the horizontal sensor 40, vertical sensor 41, and roll sensor 42. If additional corrections must be made, the hydraulic pressure can be increased or decreased by the amount necessary to correct for the drill error. Flexible pipe 79 provides for movement of housing 55 and end plate 75 by effectively decoupling the mandrel from tube 76 but yet providing a closed conduit for the flow of drilling fluids.

OTHER EMBODIMENTS FIGS. 7 and 8 illustrate other embodiments following the teachings of the above invention. FIG. 7 illustrates a helically formed pipe 100 which has a ring 63 confin- 8 ing a plurality of ball bearings 101. Ring 63 is attached to housing 55 in the manner illustrated in FIGS. 4 through 6 and functions in the identical manner. FIG. 8 illustrates a surface following the teachings of FIGS. 4 through 7 and provides a two-dimensional movement rather than a three-dimensional movement; FIG. 8 comprises a bar 103 having an upper contoured surface 104 and a lower contoured surface 105. Rollers 63 engage surfaces 104 and 105, respectively. A roller mounting means 106 journals rollers 63 and transfers the movement to a housing similar to the housing 55 disclosed in FIGS. 4 and 5.

Referring to FIG. 9, a cross-sectional portion of FIG. 4 is illustrated. The contoured surface 54 of FIG. 4 is formed into a plurality of strips and attached to the inner wall 39 of housing 55 by a pair of screws or rivets 66. An engagement means, such as roller 67, is attached to the end of piston 53 by a support surface 68. A pin 69 journals roller 67 in support surface 68. The operation of the system is substantially identical to the operation of the embodiment illustrated in FIG. 4. The contoured surface will have the same mathematical interrelationship as that disclosed for FIG. 4; however, it should be noted that as roller 67 moves toward end 96, the angular displacement of the unit 14 with respect to the axis of mandrel 50 will become less by an mount proportional to the distance moved over the surface 54 toward point 96. In order to maintain an equal angular displacement, the distance Y as defined in Tables 1 through'6 should be increased by a linear amount proportional to the distance X along surface 54.

CONCLUSIONS The directional control apparatus incorporated in a drill assembly has been disclosed which provides axial control and 360 deviation control for a drill bit. The

embodiment disclosed herein locates the directional control apparatus between the thrust unit and. the instrument module. It is obvious that other locations are feasible for the control apparatus and that other methods of utilizing same are possible. A flexible coupling, having at least .4 of a degree flexing capability, is provided between the thrust unit and the instrument package, stabilizers are attached to the drilling unit. The stabilizers will provide a fulcrum for a force generated by the deflection unit, thereby offering superior directional control capabilities.

Other obvious modifications can be made in the embodiment as disclosed in this specification and still be within the scope of the invention as disclosed in the specification and the appended claims.

We claim: 1. An apparatus for deflecting the axis of a drill assembly comprising:

a. an outer housing;

b. a piston means having spaced surfaces contoured into the surface of said piston means;

c. means for slidably mounting said piston means;

d. engaging means mounted between said housing and said piston means and in slidable contact with said spaced surfaces;

e. .means for moving said piston means along the length of its axis; and v f. means for yieldably attaching one end of said housing to said means for slidably mounting said piston means, whereby longitudinal movement of said piston means along its length will communicate the variations in said contoured surfaces to the axial position of said housing with respect to the axis of said piston means.

2. An apparatus as defined in claim 1 wherein said spaced surfaces comprise three contoured surfaces of said piston means, a cylinder wall coaxially mounted around said piston means to form a hydraulic cylinder, hydraulic inlet means to said hydraulic piston, and biasing means at the opposite end of said piston means.

5. An apparatus for deflecting the axis of a drill assembly comprising:

a. a mandrel;

b. a.tubular piston having an inner diameter dimensioned to slidably fit over said mandrel;

c. a tubular piston cylinder having one end attached to said mandrel and the other end extending over said tubular piston;

d. a first sealing means at one end of said tubular piston between said piston and said piston cylinder; e. a second sealing means between said tubular piston and said mandrel;

f. hydraulic fluid inlet means to said first-mentioned end of said tubular piston;

g. spring biasing means between said mandrel and the remaining end of said tubular piston;

h. outer housing means;

i. means for yieldably attaching said outer housing means to said mandrel;

j. contour means formed in the outer surface of said tubular piston; and 1 k. engaging means mounted to said housing means and moveably engaging said contour means whereby hydraulic pressure applied to the end of said tubular piston will force said tubular piston along the length of said mandrel against the force created by said biasing means, said engaging means following the contour means thereby positioning the axis of said outer housing with respect 'to the axis of said mandrel in accordance with the configuration of said contour means.

6. An apparatus as defined in claim 5 wherein said contour means comprises two surfaces placed directly opposite each other on said tubular piston.

7. An apparatus as defined in claim 5 wherein said contour means comprises three surfaces formed in the outer surface of said tubular piston, said contour means being spaced equal distance from each other about the outer circumference of said tubular piston. v

8. An apparatus as defined in claim 7 wherein said contour surfaces are formed in accordance with the mathematical interrelationship as defined in Tables I through 6.

9. An apparatus as defined in claim 8 wherein said engaging means comprises a ring having its outer periphery rigidly attached to said outer housing and three rollers journaled on the inner periphery of said ring and dimensioned to engage said three contour surfaces.

10. An apparatus for deflecting the axis of a drill assembly comprising:

a. an outer housing;

b. a deflection means having a contoured surface means;

c. engaging means mounted between said outer housing and said deflection means and in slidable contact with said contoured surface means;

d. means for positioning said contoured surface means with respect to said engaging means to cause a resultant deflection in the housing axis with respect to said deflection means; and

. e. means for yieldably attaching said outer housing to said deflection means.

11. An apparatus for deflecting the axis of a drill assembly as described in claim 10 wherein said deflection means comprises a bar having a rectangular cross section and wherein said contoured surfaces are opposite each other.

12. An apparatus for deflecting the axis of a drill assembly as described in claim 10 wherein said deflection means comprises a cylinder having an outer circumference in the configuration of a helix.

13. An apparatus for deflecting the axis of a drill assembly as defined in claim 10 wherein said deflection means comprises a plurality of contoured surfaces, means for attaching said contoured surfaces to said outer housing means, and wherein said engaging means is mounted to said means for positioning the said contoured surface means with respect to said engaging means.

14. An apparatus for deflecting the axis of a drill assembly as described in claim 10 wherein said deflection means comprises a cylinder having three contoured surfaces spaced l20 apart around the circumference of said cylinder.

15. A device as described in claim l4 wherein said contoured surfaces have the mathematical inner relationship as defined in Tables 1 through 6 when said contoured surfaces are formed by a milling cutter having a diameter of 0.25 inch and wherein said engaging means comprises a plurality of rollers in contact with said contoured surfaces and wherein the diameter of said rollers is 0.25 inch.

16. An apparatus for deflecting the axis of a drill as sembly comprising:

a. a mandrel;

b. a tubular piston having an inner diameter dimensioned to slidably fit over said mandrel;

c. a tubular piston cylinder having one end attached to said mandrel and the other end extending over said tubular piston;

d.' a first sealing means at one end of said tubular piston between said piston and said piston cylinder;

e. a second sealing means between said tubualr piston and said mandrel;

f. hydraulic fluid inlet means to said first-mentioned end'of said tubular piston;

g. spring biasing means between said mandrel and the remaining end of said tubular piston;

h. outer housing means;

i. means for yieldably attaching said outer housing .means to said mandrel;

j. contour means attached to said housing means;

k. engaging means mounted to said tubular piston and movably engaging said contour means whereby hydraulic pressure applied to the end of said tubular piston will force said tubular piston along the length of said mandrel against the force created by said biasing means, said engaging means following the contour means thereby positioning the axis of said outer housing with respect to the axis of said mandrel in accordance with the configuration of said contour means.

17. An apparatus for deflecting the axis of a. drill assembly as defined in claim 16 wherein said contour means comprises two surfaces placed directly opposite a milling cutter having a diameter of 0.25 inch and wherein said engaging means comprises a roller in Contact with each surface having a diameter of 0.25

inch. 

1. An apparatus for deflecting the axis of a drill assembly comprising: a. an outer housing; b. a piston means having spaced surfaces contoured into the surface of said piston means; c. means for slidably mounting said piston means; d. engaging means mounted between said housing and said piston means and in slidable contact with said spaced surfaces; e. means fOr moving said piston means along the length of its axis; and f. means for yieldably attaching one end of said housing to said means for slidably mounting said piston means, whereby longitudinal movement of said piston means along its length will communicate the variations in said contoured surfaces to the axial position of said housing with respect to the axis of said piston means.
 2. An apparatus as defined in claim 1 wherein said spaced surfaces comprise three contoured surfaces spaced equal distance from each other around the circumference of said piston means and having interrelationship as defined in Tables 1 through
 6. 3. An apparatus as defined in claim 2 wherein said engaging means comprises a ring having three rollers positioned to engage said three contoured surfaces and wherein the outer circumference of said ring is mounted to said outer housing.
 4. An apparatus as defined in claim 3 wherein said means for moving said piston means along the length of its axis comprises a hydraulic piston formed at the end of said piston means, a cylinder wall coaxially mounted around said piston means to form a hydraulic cylinder, hydraulic inlet means to said hydraulic piston, and biasing means at the opposite end of said piston means.
 5. An apparatus for deflecting the axis of a drill assembly comprising: a. a mandrel; b. a tubular piston having an inner diameter dimensioned to slidably fit over said mandrel; c. a tubular piston cylinder having one end attached to said mandrel and the other end extending over said tubular piston; d. a first sealing means at one end of said tubular piston between said piston and said piston cylinder; e. a second sealing means between said tubular piston and said mandrel; f. hydraulic fluid inlet means to said first-mentioned end of said tubular piston; g. spring biasing means between said mandrel and the remaining end of said tubular piston; h. outer housing means; i. means for yieldably attaching said outer housing means to said mandrel; j. contour means formed in the outer surface of said tubular piston; and k. engaging means mounted to said housing means and moveably engaging said contour means whereby hydraulic pressure applied to the end of said tubular piston will force said tubular piston along the length of said mandrel against the force created by said biasing means, said engaging means following the contour means thereby positioning the axis of said outer housing with respect to the axis of said mandrel in accordance with the configuration of said contour means.
 6. An apparatus as defined in claim 5 wherein said contour means comprises two surfaces placed directly opposite each other on said tubular piston.
 7. An apparatus as defined in claim 5 wherein said contour means comprises three surfaces formed in the outer surface of said tubular piston, said contour means being spaced equal distance from each other about the outer circumference of said tubular piston.
 8. An apparatus as defined in claim 7 wherein said contour surfaces are formed in accordance with the mathematical interrelationship as defined in Tables 1 through
 6. 9. An apparatus as defined in claim 8 wherein said engaging means comprises a ring having its outer periphery rigidly attached to said outer housing and three rollers journaled on the inner periphery of said ring and dimensioned to engage said three contour surfaces.
 10. An apparatus for deflecting the axis of a drill assembly comprising: a. an outer housing; b. a deflection means having a contoured surface means; c. engaging means mounted between said outer housing and said deflection means and in slidable contact with said contoured surface means; d. means for positioning said contoured surface means with respect to said engaging means to cause a resultant deflection in the housing axis with respect to said deflection means; and e. means for yieldably attaching said outer housing To said deflection means.
 11. An apparatus for deflecting the axis of a drill assembly as described in claim 10 wherein said deflection means comprises a bar having a rectangular cross-section and wherein said contoured surfaces are opposite each other.
 12. An apparatus for deflecting the axis of a drill assembly as described in claim 10 wherein said deflection means comprises a cylinder having an outer circumference in the configuration of a helix.
 13. An apparatus for deflecting the axis of a drill assembly as defined in claim 10 wherein said deflection means comprises a plurality of contoured surfaces, means for attaching said contoured surfaces to said outer housing means, and wherein said engaging means is mounted to said means for positioning the said contoured surface means with respect to said engaging means.
 14. An apparatus for deflecting the axis of a drill assembly as described in claim 10 wherein said deflection means comprises a cylinder having three contoured surfaces spaced 120* apart around the circumference of said cylinder.
 15. A device as described in claim 14 wherein said contoured surfaces have the mathematical inner relationship as defined in Tables 1 through 6 when said contoured surfaces are formed by a milling cutter having a diameter of 0.25 inch and wherein said engaging means comprises a plurality of rollers in contact with said contoured surfaces and wherein the diameter of said rollers is 0.25 inch.
 16. An apparatus for deflecting the axis of a drill assembly comprising: a. a mandrel; b. a tubular piston having an inner diameter dimensioned to slidably fit over said mandrel; c. a tubular piston cylinder having one end attached to said mandrel and the other end extending over said tubular piston; d. a first sealing means at one end of said tubular piston between said piston and said piston cylinder; e. a second sealing means between said tubualr piston and said mandrel; f. hydraulic fluid inlet means to said first-mentioned end of said tubular piston; g. spring biasing means between said mandrel and the remaining end of said tubular piston; h. outer housing means; i. means for yieldably attaching said outer housing means to said mandrel; j. contour means attached to said housing means; k. engaging means mounted to said tubular piston and movably engaging said contour means whereby hydraulic pressure applied to the end of said tubular piston will force said tubular piston along the length of said mandrel against the force created by said biasing means, said engaging means following the contour means thereby positioning the axis of said outer housing with respect to the axis of said mandrel in accordance with the configuration of said contour means.
 17. An apparatus for deflecting the axis of a drill assembly as defined in claim 16 wherein said contour means comprises two surfaces placed directly opposite each other on said outer housing means.
 18. An apparatus for deflecting the axis of a drill assembly as defined in claim 16 wherein said contour means comprises three surfaces formed in the inner surface of said outer housing means, said contour means being spaced 120* from each other as measured from the axis of said mandrel.
 19. An apparatus for deflecting the axis of a drill assembly as defined in claim 18 wherein said contour surfaces are formed in accordance with the mathematical inner relationship as defined in Tables 1 through 6 by a milling cutter having a diameter of 0.25 inch and wherein said engaging means comprises a roller in contact with each surface having a diameter of 0.25 inch. 